{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2025 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# assignment_with_constraints_sat"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/examples/assignment_with_constraints_sat.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/examples/python/assignment_with_constraints_sat.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "solve an assignment problem with combination constraints on workers.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Sequence\n",
    "from ortools.sat.python import cp_model\n",
    "\n",
    "\n",
    "def solve_assignment():\n",
    "    \"\"\"solve the assignment problem.\"\"\"\n",
    "    # Data.\n",
    "    cost = [\n",
    "        [90, 76, 75, 70, 50, 74],\n",
    "        [35, 85, 55, 65, 48, 101],\n",
    "        [125, 95, 90, 105, 59, 120],\n",
    "        [45, 110, 95, 115, 104, 83],\n",
    "        [60, 105, 80, 75, 59, 62],\n",
    "        [45, 65, 110, 95, 47, 31],\n",
    "        [38, 51, 107, 41, 69, 99],\n",
    "        [47, 85, 57, 71, 92, 77],\n",
    "        [39, 63, 97, 49, 118, 56],\n",
    "        [47, 101, 71, 60, 88, 109],\n",
    "        [17, 39, 103, 64, 61, 92],\n",
    "        [101, 45, 83, 59, 92, 27],\n",
    "    ]\n",
    "\n",
    "    group1 = [\n",
    "        [0, 0, 1, 1],  # Workers 2, 3\n",
    "        [0, 1, 0, 1],  # Workers 1, 3\n",
    "        [0, 1, 1, 0],  # Workers 1, 2\n",
    "        [1, 1, 0, 0],  # Workers 0, 1\n",
    "        [1, 0, 1, 0],  # Workers 0, 2\n",
    "    ]\n",
    "\n",
    "    group2 = [\n",
    "        [0, 0, 1, 1],  # Workers 6, 7\n",
    "        [0, 1, 0, 1],  # Workers 5, 7\n",
    "        [0, 1, 1, 0],  # Workers 5, 6\n",
    "        [1, 1, 0, 0],  # Workers 4, 5\n",
    "        [1, 0, 0, 1],  # Workers 4, 7\n",
    "    ]\n",
    "\n",
    "    group3 = [\n",
    "        [0, 0, 1, 1],  # Workers 10, 11\n",
    "        [0, 1, 0, 1],  # Workers 9, 11\n",
    "        [0, 1, 1, 0],  # Workers 9, 10\n",
    "        [1, 0, 1, 0],  # Workers 8, 10\n",
    "        [1, 0, 0, 1],  # Workers 8, 11\n",
    "    ]\n",
    "\n",
    "    sizes = [10, 7, 3, 12, 15, 4, 11, 5]\n",
    "    total_size_max = 15\n",
    "    num_workers = len(cost)\n",
    "    num_tasks = len(cost[1])\n",
    "    all_workers = range(num_workers)\n",
    "    all_tasks = range(num_tasks)\n",
    "\n",
    "    # Model.\n",
    "\n",
    "    model = cp_model.CpModel()\n",
    "    # Variables\n",
    "    selected = [\n",
    "        [model.new_bool_var(f\"x[{i},{j}]\") for j in all_tasks] for i in all_workers\n",
    "    ]\n",
    "    works = [model.new_bool_var(f\"works[{i}]\") for i in all_workers]\n",
    "\n",
    "    # Constraints\n",
    "\n",
    "    # Link selected and workers.\n",
    "    for i in range(num_workers):\n",
    "        model.add_max_equality(works[i], selected[i])\n",
    "\n",
    "    # Each task is assigned to at least one worker.\n",
    "    for j in all_tasks:\n",
    "        model.add(sum(selected[i][j] for i in all_workers) >= 1)\n",
    "\n",
    "    # Total task size for each worker is at most total_size_max\n",
    "    for i in all_workers:\n",
    "        model.add(sum(sizes[j] * selected[i][j] for j in all_tasks) <= total_size_max)\n",
    "\n",
    "    # Group constraints.\n",
    "    model.add_allowed_assignments([works[0], works[1], works[2], works[3]], group1)\n",
    "    model.add_allowed_assignments([works[4], works[5], works[6], works[7]], group2)\n",
    "    model.add_allowed_assignments([works[8], works[9], works[10], works[11]], group3)\n",
    "\n",
    "    # Objective\n",
    "    model.minimize(\n",
    "        sum(selected[i][j] * cost[i][j] for j in all_tasks for i in all_workers)\n",
    "    )\n",
    "\n",
    "    # Solve and output solution.\n",
    "    solver = cp_model.CpSolver()\n",
    "    status = solver.solve(model)\n",
    "\n",
    "    if status == cp_model.OPTIMAL:\n",
    "        print(f\"Total cost = {solver.objective_value}\")\n",
    "        print()\n",
    "        for i in all_workers:\n",
    "            for j in all_tasks:\n",
    "                if solver.boolean_value(selected[i][j]):\n",
    "                    print(f\"Worker {i} assigned to task {j} with Cost = {cost[i][j]}\")\n",
    "\n",
    "        print()\n",
    "\n",
    "    print(solver.response_stats())\n",
    "\n",
    "\n",
    "def main(argv: Sequence[str]) -> None:\n",
    "    if len(argv) > 1:\n",
    "        raise app.UsageError(\"Too many command-line arguments.\")\n",
    "    solve_assignment()\n",
    "\n",
    "\n",
    "main()\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "name": "python"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
